MathDB

8

Part of 2021 Indonesia MO

Problems(1)

Find the number of horizontal and vertical triminoes used to tile

Source: Indonesia National Math Olympiad 2021 Problem 8 (INAMO 2021/8)

11/9/2021
On a 100×100100 \times 100 chessboard, the plan is to place several 1×31 \times 3 boards and 3×13 \times 1 board, so that
[*] Each tile of the initial chessboard is covered by at most one small board. [*] The boards cover the entire chessboard tile, except for one tile. [*] The sides of the board are placed parallel to the chessboard.
Suppose that to carry out the instructions above, it takes HH number of 1×31 \times 3 boards and VV number of 3×13 \times 1 boards. Determine all possible pairs of (H,V)(H,V).
Proposed by Muhammad Afifurrahman, Indonesia
combinatoricsgridboardtrimino